Applied Physics and Applied Mathematics
Why Get your Master's in Quantum Science and Technology at Columbia?
Columbia Engineering provides a rigorous Ivy League education in an atmosphere charged with innovation in the heart of a dynamic global city.
As a student here, you’ll benefit from:
- Incredible Research Environment:
Join a rich community of exploration and innovation across schools and departments, including the Columbia Quantum Initiative, the School of Engineering, and the Center for Computational Quantum Physics, with scores of researchers working on areas ranging from quantum computing to photonics to quantum materials.
- Strategic Partnerships
Benefit from Colombia's position within a network of universities, research organizations, and industry partners through the Columbia Quantum Initiative to access extended opportunities for research, internships, and job connections.
- Multi-Disciplinary Expertise:
Learn from active scholars and researchers within several departments of the School of Engineering and the Department of Physics, gaining insights and perspectives from diverse fields for a broad career preparation.
- Flexible Curriculum:
Choose to focus your training in areas that match your career objectives, including quantum computing, photonics, and nanoscale technology, with a selection of electives within Engineering and Physics tracks.
Research Areas
- Computational Science and Engineering
- Numerical Analysis
- Partial Differential Equations
- Computational Fluid Dynamics
- Computational Solid Earth Science
- Computational Thermodynamics
Additional Information
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Honors & Awards
- Society of Columbia Graduates' Great Teacher Award in Columbia College for the 2022/2023
- Fellow of the American Geophysical Union (AGU) 2022
- Columbia Engineering Alumni Association's Distinguished Faculty Teaching Award 2020
- SEAS Alumni Teaching Award 2004
- SEAS Kim Award 2004
- DEES Outstanding Teaching Award 1998 & 2002
- Marshall Scholar 1985
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Professional Experience
- Professor, DEES/APAM Columbia University, 2008
- Associate Professor, DEES/APAM, Columbia University, 2000-2008
- Storke-Doherty Lecturer, Lamont-Doherty Earth Observatory, Columbia University, 1997-1999
Additional Information
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Professional Experience
Columbia University, New York, NY:
- APAM Department Chair (July 2012 - June 2018)
- Professor of Materials Science and Engineering (2004 - Present)
- Adjunct Professor (1985 - 2004)
International Business Machines Corporation, Yorktown Heights, NY:
- Research Consultant (2004 - 2017)
- Research Staff Member (1987 - 2004)
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Education
- PhD, Materials Sci. & Engineering, Northwestern University
- BSci., Metallurgical Engineering, Middle East Technical University
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Professional Affiliations
- Fellow, American Physical Society
- Member ASM, TMS-AIME, ACA, APS, Sigma Xi, IEEE, ICDD
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Honors & Awards
- Hanawalt Award for rigorous physical modeling of the scattering processes from nanocrystalline materials, International Centre for Diffraction Data, 2019
- Jenkins Lifetime Achievement Award, International Centre for Diffraction Data, 2015
- Blackall Machine Tool and Gage Award, American Society of Mechanical Engineers, 2006
- Two IBM Outstanding Technical Achievement Awards for research and development of computer and packaging structures
- IBM Research Division Award for research on diffusion barriers and 11 IBM Invention Plateaus for filed patents
- Adjunct Faculty Award for Excellence in Teaching, Columbia University, 1993
Research Areas
- Nanoscale Magnetic Films and Heterostructures
- Materials Issues in Spin-Polarized Transport
- Materials Engineering of Magnetic Dynamics
- Materials
Additional Information
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Professional Experience
- NRC Postdoctoral Fellow, National Institute of Standards and Technology, Magnetic Technology Division, Boulder CO 1999-2001
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Honors & Awards
- NSF Career (2003)
- ARO Young Investigator (2002)
Research Areas
- Microlocal Analysis
- Computation in Learning
Additional Information
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Professional Experience
- Lecturer in Discipline, Columbia University, 2017–
- Clinical Assistant Professor of Mathematics, New York University, 2012–2017
- Assistant Professor of Mathematics, Bard High School Early College, 2007–2012
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Honors & Awards
- Newton Fellow, Math for America, 2006–2011
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Education
- PhD, Mathematics, Northwestern University
- MA, Mathematics Education, New York University
- MA, Mathematics, Stony Brook University
- BS, Applied Mathematics, Columbia University
Research Areas
- Plasma Physics (Controlled Fusion)
Additional Information
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Professional Experience
- Thomas Alva Edison Professor of Applied Physics, Columbia University, 2004–
- Interim Dean, School of Engineering and Applied Science, Columbia University, 2007–2009
- Chairman of Applied Physics and Applied Mathematics, Columbia University, 1988 –1994 and 1997–2000
- Vice-Dean, School of Engineering and Applied Science, Columbia University, 1994-1995
- Professor of Applied Physics, Columbia University, 1988–2004
- Associate Professor of Applied Physics, Columbia University, 1983–1988
- Assistant Professor of Applied Physics, Columbia University, 1978–1983
- Assistant Professor of Engineering science, Columbia University, 1977–1978
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Professional Affiliations
- American Physical Society
- University Fusion Association
- Fusion Power Associates
- European Physical Society
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Honors & Awards
- Alfred P. Sloan Research Fellow in Physics, 1984-86
- Fellow of the American Physical Society, 1989
- Leadership Award from Fusion Power Associates, 2006
- American Physical Society John Dawson Award for Excellence in Plasma Physics, 2007
- Distinguished Career Award from Fusion Power Associates, 2023
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Education
- PhD, Plasma Physics, University of Wisconsin-Madison
- MS, Nuclear Engineering, University of Wisconsin-Madison
- BS, Physics, California Institute of Technology
Research Areas
- Materials for Energy
- Materials for Environmental Applications
- Materials Synthesis and Processing
- Nanomaterials
- Biomaterials
- SiGe BiCom Misfit Dislocation Avoidance
- Ceramic Superconductors
- Grain Boundaries and Interfaces
Additional Information
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Professional Affiliations
- American Ceramic Society
- American Chemical Society
- ASM International
- Association for Iron & Steel Technology (AIST)
- Materials Research Society
- The Minerals, Metals, Materials Society (TMS)
- American Physical Society
- Society of Women Engineers
- International Committee of Diffraction Data
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Honors & Awards
- Fellow of American Physical Society, 2018
- Avanessians Diversity Award, 2012
- BASF Catalysis Research Award, 2008-2011
- American Ceramic Society Fellow, 2008
- Advance Fellow: National Science Foundation/Univ. of Washington, 2004
- Tan Chin Tuan Fellow, 2004
- Guggenheim Fellow, 2003
- IBM Faculty Award, 1998
- Outstanding Woman Scientist Award, 1997
- Presidential Faculty Fellow from the White House and the National Science Foundation, 1993
- Very Important Parent: Luther Lee Emerson School in Demarest, NJ, 1992
- DuPont Faculty Award, 1991, 1992
- Sigma Xi, 1982
- Tau Beta Pi, 1979
- Columbia Univ. SEAS Francis B.F. Rhodes Prize 1980
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Professional Experience
- Professor of materials science and engineering in the Department of Applied Physics and Mathematics, Columbia Engineering, 2002 –
- Co-chair of the Solid State Program, Columbia Engineering, 2001 –2005
- Executive committee member and outreach director, Materials Research Science & Engineering Center, 1998-2009
- Associate professor of applied physics and applied mathematics, Columbia Engineering, 1998 – 2000
- Co-chair of Materials Science and Engineering Program and Committee, Columbia Engineering, till 1999
- Associate professor of chemical engineering and materials, 1993 – 1998
- Associate professor of metallurgy and materiais, 1990 – 1993
- Visiting professor of materials, as Tan Fellow, Nanyang Technological Univ. (Singapore), 2004
- Visiting professor of materials science and engineering, as National Science Foundation 2004 Advanced Fellow, University of Washington.
- Visiting professor of physics, Guggenheim Fellow, University of California San Diego, 2004
- Visiting scientist, IBM Watson Research Lab, 1999
- Visiting scientist, Bitter Magnet Lab, 1993 – 1996
- Member of technical staff, Superconductors, and Surface Modifications to solve the last-mile-problem, Bell-Labs & Bellcore, Murray Hill, NJ, 1985-1990
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Education
- ScD, Materials Science, Massachusetts Institute of Technology
- BS, Metallurgy and Materials Science, Columbia Unversity
Additional Information
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Professional Experience
- Assistant Professor of Applied Physics, Columbia University, 2024-
- Postdoctoral Research Scientist, Department of Physics, Columbia University, 2021-2023
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Honors & Awards
- Moore Fellow in Materials Synthesis, 2024-
- Junior Fellow, Simons Society of Fellows, 2021-2023
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Education
- PhD, Physics, Massachusetts Institute of Technology
- BS, Applied Sciences and Engineering, Rutgers University
Research Areas
- Computational Science and Engineering
- Control Theory
- Real and Complex Analysis
- Harmonic Analysis
- Approximation Theory
- Functional Analysis and Operator Theory
- Geometry and Topology
- Numerical Analysis
- Partial Differential Equations
- Geometric Analysis
- Numerical Analysis
- Novel Wave Phenomena in Heterogeneous, Nonlinear, and Random Media
Additional information
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Professional Experience
- Professor of Mathematics, Columbia University, 2014-present
- Professor of Applied Mathematics, SEAS, Columbia University 2004-present,
- MTS-Fundamental Mathematics Research Department, Bell Laboratories, Lucent Technologies, 1998-2004
- Professor of Mathematics, University of Michigan, Ann Arbor, 1993-2000
- Associate Professor of Mathematics (tenured) University of Michigan, Ann Arbor, 1988-1993
- Assistant Professor of Mathematics, Princeton University, 1984-1988
- NSF Postdoctoral Fellow, Stanford University, 1982-1984
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Honors & Awards
- Elected to the American Academy of Arts and Sciences, 2025
- Simons Foundation Math + X Investigator Award, 2015-2025
- Martin D. Kruskal Prize, SIAM 2018
- Fellow of the AMS, 2014
- SIAM Fellow, 2010
Research Areas
- Soft Matter
- Advanced Materials
- Nanotechnology
- Advanced Materials
- Materials Characterization
- Materials Design and Engineering
- Materials Synthesis and Processing
- Nanomaterials
- Advanced Manufacturing
- Biocompatible Materials
- Bioinductive Materials
- Biomimetic Materials
- Functional and Responsive Materials
- Nanomaterials (Nanotechnology)
- Biomaterials
Additional Information
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Professional Experience
- Professor, Department of Chemical Engineering, Columbia University, 2016–
- Professor, Department of Applied Physics and Applied Mathematics, Columbia University, 2016–
- Group leader for Soft and Bionanomaterials, Center for Functional Nanomaterials, Brookhaven National Laboratory, 2008-
- Staff Scientist, Center for Functional Nanomaterials, Brookhaven National Laboratory, 2004–2016
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Professional Affiliations
- American Physical Society
- Material Research Society
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Honors & Awards
- Vannevar Bush Faculty Fellow, 2024
- Battelle Inventor of the Year, 2016
- Elected Fellow of the American Physical Society 2014
- BNL Science and Technology Award for Outstanding Achievements 2011
- Gordon Battelle Prize for Scientific Discovery, 2010
- Department of Energy Outstanding Mentor Award, 2009
- Rothschild Foundation Distinguished Fellowship, 2000
- Wolf Foundation Scholarship for outstanding PhD research, 1997
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Education
- Rothschild Postdoctoral Fellow, Applied Physics, Harvard University
- PhD, Physics, Bar-Ilan University
- MS, Physics, Bar-Ilan University
Research Areas
- Atmospheric, Ocean, and Earth Physics
- Condensed Matter Physics
- Solid-State Physics
- Energy Science
- Quantum Materials
- Advanced Materials
- Energy, Mineral, and Materials
- Sustainable Production of Earth Mineral and Metal Resources
- Materials Modeling and Simulation
- Planetary Materials Simulation and Discovery
Additional Information
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Professional Experience
- Professor of Applied Physics and Applied Mathematics, Columbia University, 2017
- Professor of Earth and Environmental Science, Lamont Doherty Earth Observatory, Columbia University, 2017-
- Member of the graduate faculty in School of Physics and Astronomy (1996-2016), Department of Earth Science (2010-2016), Chemical Physics Program (1996-2016), Scientific Computing Program (1996-2016), University of Minnesota, 1996-2016
- Founding director, Virtual Laboratory for Earth and Planetary Materials, University of Minnesota, 2004
- Professor of Materials Science, Department of Chemical Engineering and Materials Science, University of Minnesota, 2006-2016
- Associate Professor of Materials Science, Department of Chemical Engineering and Materials Science, University of Minnesota, 2001-2006
- Assistant Professor of Materials Science, Department of Chemical Engineering and Materials Science, University of Minnesota, 1994-2001
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Professional Affiliations
- American Physical Society
- American Geophysical Union
- Mineralogical Society of America
- American Association for Advancement of Science
- Materials Research Society
- American Academy of Arts and Sciences
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Honors & Awards
• Bridgman Award of the International Association for Advancement of Research in High Pressure Science and Technology (AIRAPT) (2025) (first woman)
• Harry Hess Visiting Professorship at Princeton University, 2024
• President-Elect, President, Past-President, Mineral and Rock Physics Section, American Geophysical Union, 2023 - 2028
• Vice-Chair, Chair-Elect, Chair, Past-Chair, Division of Computational Physics, American Physical Society, 2017 - 2020
•Outstanding Referee for Physical Review B, 2021
• Wilhelm Heraeus Visiting Professorship Award, University of Frankfurt, 2015 - 2016
• Member, American Academy of Arts and Sciences, 2013-
• Fellow, American Association for Advancement of Science (Physics), 2012-
• Fellow, Mineralogical Society of America, 2009-
• Fellow, American Geophysical Union, 2008-
• Fellow, American Physical Society, Division of Materials Physics, 2006-
• Alexander von Humboldt Research Award for Senior US Scientists, 2008
• Japan Society for Progress of Science (JSPS), Invitation Fellowship for Research in Japan, 2008
• Member at-large, American Physical Society, Division of Computational Physics, 2000 - 2003
• Fellow (2001-) and Associate Fellow (1997-2001) of Minnesota Supercomputing Institute
• Shell Land-Grant Professor in Chemical Engineering and Material Science, University of Minnesota, 1994 - 1995
• Honorary Research Fellow, Birkbeck College, University of London, UK, 1993 - 1994
• Fellowships from Brazilian agencies:
- São Paulo State Research Foundation, FAPESP (undergraduate, 1978-80), with Sueli Aldrovandi (Astrophysics, Institute for Astronomy and Geophysics, University of São Paulo)
- National Research Council for Nuclear Energy, CNEN (MSc, 1980-82), with José Roberto Leite (Physics, Nuclear Energy Research Institute, University of São Paulo)
- National Research Council, CNPq (PhD, 1983-87) with Marvin L. Cohen (Physics, UC-Berkeley)
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Selected Publications
250. L. Wei, K.-M. Ho, R. M. Wentzcovitch, Y. Sun, The Fe-Ni phase diagram and the Earth’s inner core structure, Science Advances11, eadu1998. DOI 10.1126/sciadv.adu1998(2025). https://arxiv.org/pdf/2503.21493
247. H. Wang, C. Luo, and R. M. Wentzcovitch, Machine learning potentials for serpentines, J. Geophys. Res. Machine Learning and Computations1, e2024JH000434. DOI: 10.1029/2024JH000434 (2024). https://arxiv.org/pdf/2409.16402
245. Z. Zhuang and R. Wentzcovitch, Fe2+ partitioning in Al-free pyrolite: consequences for seismic velocities and heterogeneities, Geophys. Res. Lett.51, e2024GL108967 (2024). DOI: 10.1029/2024GL108967 https://arxiv.org/pdf/2405.11830
243. F. Wu, Y. Sun, T. Wan, S. Wu, and R. M. Wentzcovitch, Deep-learning-based prediction of the tetragonal to cubic transition in davemaoite, Geophys. Res. Lett. 51, e2023GL108012 (2024). DOI: 10.1029/2023GL108012 https://arxiv.org/html/2401.14588v1
239. L. Cobden, J. Zhuang, W. Lei, R. M. Wentzcovitch, J. Trampert, and J. Tromp, Full-waveform tomography reveals iron spin crossover in Earth’s lowermantle, Nature Communications15, 1961 (2024). DOI: 10.1038/s41467-024-46040-1 https://arxiv.org/abs/2303.05476
234. Z. Zhang, Y. Sun, and R. M. Wentzcovitch, PBE-GGA predicts the B8↔B2 phase boundary of FeO under Earth’s core pressures,Proc. Nat. Acad. Sc. USA120, e2304726120 (2023). DOI: 10.1073/pnas.2304726120 https://arxiv.org/abs/2211.15052
230. Q. Zhang, C. Gu, J. Zhuang, and R. M. Wentzcovitch, express: extensible, high-level workflows for swifter ab initio materials modeling, Comp. Phys. Comm., 108515 (2023). DOI: 10.1016/j.cpc.2022.108515 https://arxiv.org/abs/2109.11724
229 J. Liu, Y. Sun, C. Lv, F. Zhang, S. Fu, V. B. Prakapenka, C.-Z. Wang, K.-M. Ho, J.-F. Lin, R. M. Wentzcovitch, Iron-rich Fe-O compounds at Earth's core pressures, The Innovation 4, 100354, (2023). DOI: 10.1016/J.XINN.2022.100354 https://arxiv.org/abs/2110.00524
219. Y. Sun, F. Zhang, M. Y. Mendelev, R. M. Wentzcovitch, K.-M. Ho, Two-step nucleation of the Earth's inner core, Proceedings of the National Academy of Sciences of the USA, 119, e2113059199, (2022). DOI: 10.1073/pnas.2113059119 https://arxiv.org/abs/2105.07296
218. Z. Zhang, D.-B. Zhang, K. Onga, K. Ohta, K. Hirose, R. M. Wentzcovitch, Thermal conductivity of cubic CaSiO3–perovskite at lower mantle conditions, Phys. Rev. B104, 184101, (2021).DOI: 10.1103/PhysRevB.104.184101 https://arxiv.org/abs/2005.08289s
216. G. Shephard, C. Houser, J. Hernlund, J. Valencia-Cardona, R. Tronne, and R. M. Wentzcovitch, Seismic detection of the iron spin transition in Earth's lower mantle, Nature Communications 12, 5905 (2021). DOI: 10.1038/s41467-021-26115-z https://eartharxiv.org/repository/view/133/
215. C. Luo, X. Deng, W. Wang, G. Shukla, Z. Wu, and R. M. Wentzcovitch, cij: a Python code for quasiharmonic thermoelasticity, Comp. Phys. Comm. 267, 108067 (2021). DOI: 10.1016/j.cpc.2021.108067 https://arxiv.org/abs/2101.12596
214. K. Umemoto and R. M. Wentzcovitch, Ab initio prediction of an order-disorder transition in Mg2GeO4: implication for the nature of Super-Earth's mantles, Phys.Rev. Materials5, 093604 (2021). DOI: 10.1103/PhysRevMaterials.5.093604 http://arxiv.org/abs/2012.08056
207. M. Marcondes, F. Zhang, and R. M. Wentzcovitch, Phonons in (Mg,Fe)O ferropericlase throughout the iron spin crossover, Phys. Rev. B102, 104112 (2020). DOI: 10.1103/PhysRevB.102.104112 https://arxiv.org/abs/2003.12348
205. W. Wang, Y. Xu, D. Sun, S. Ni, R. M. Wentzcovitch, and Z. Wu, Velocity and density characteristics of subducted oceanic crust and the origin of seismic heterogeneities in the lower mantle, Nature Communications 11, 1-7 (2020). DOI:10.1038/s41467-019-13720-2
Research Areas
- Atomic, Molecular, and Optical (AMO) Physics
- Photonics and Optics
- Quantum Information Science
- Quantum Materials
- Communications
- Electromagnetics
- Photonics
- Signal Processing
- Energy Efficiency and Conservation Technology
- Quantum Communications
- Quantum Computing
Additional information
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Professional Experience
- David M. Rickey Professor of Applied Physics and Materials Science, Columbia University, 2015 –
- Samuel B. Eckert Professor of Engineering, School of Applied and Engineering Physics, Cornell University, 2013 – 2015
- Founding Editor-in-Chief, Optica, Optical Society of America, 2013 –
- Director, School of Applied and Engineering Physics, Cornell University, 2011 – 2014
- Co-founded PicoLuz, Inc. (with Michal Lipson and Alex Cable), 2010
- Director, NSF Center for Nanoscale Systems in Information Technologies, Cornell University, 2007-2012
- Associate Director, School of Applied and Engineering Physics, Cornell University, 2006 – 2007
- Editorial Board, Laser Physics Letters, 2005 - 2009
- Editorial Board, New Journal of Physics, 2005 - 2008
- Professor, School of Applied and Engineering Physics, Cornell University, 2004 – 2013
- Director of Graduate Studies, School of Applied and Engineering Physics, Cornell University, 1999 – 2004
- Associate Professor, School of Applied and Engineering Physics, Cornell University, 1998 – 2004
- Assistant Professor, School of Applied and Engineering Physics, Cornell University, 1992 – 1998
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Professional Affiliations
- Member, Long-Term Publications Group, Optical Society of America, 2010-2012
- Director-at-Large, Board of Directors, Optical Society of America, 2008-2010
- I. Rabi Prize Committee of the American Physical Society, 2007-2010
- Member, Strategic Planning Committee, Optical Society of America, 2006-2008
- Chair, Science and Engineering Council Optical Society of America, 2004-2006
- Executive Committee, Member-at-Large, Division of Laser Science, American Physical Society, 2004-2005
- Chair, Division of Quantum Electronics, Optical Society of America, term 2000-2002
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Honors & Awards
- Arthur L. Schawlow Prize in Laser Science, 2026
- Stephen D. Fantone Distinguished Service Award, Optica, 2023
- Highly Cited Researcher for 2019
- Charles H. Townes Award, Optical Society of America, 2019
- Fellow of the IEEE
- Fellow of the American Physical Society
- Fellow of the Optical Society of America
- College of Engineering Teaching Award, 1997, 2000, 2003, and 2007
- Army Research Office Young Investigator Award, 1995
- Office of Naval Research Young Investigator Award, 1993